Linesearch-free adaptive Bregman proximal gradient for convex minimization without relative smoothness

This paper introduces adaptive Bregman proximal gradient algorithms forsolving convex composite minimization problems without relying on globalrelative smoothness or strong convexity assumptions. Building upon recentadvances in adaptive stepsize selections, the proposed methods generatestepsizes based on local curvature estimates, entirely eliminating the need forbacktracking linesearch. A key innovation is a Bregman generalization ofYoung's inequality, which allows controlling a critical inner product in termsof the same Bregman distances used in the updates. Our theory applies toproblems where the differentiable term is merely locally smooth relative to adistance-generating function, without requiring the existence of global modulior symmetry coefficients. Numerical experiments demonstrate their competitiveperformance compared to existing approaches across various problem classes.